1. Field of Invention
The present application is directed towards systems and method for simulating the evaporation of a droplet.
2. Description of Related Art
The industrial printing process includes the production of small ink droplets. Each ink droplet may contain a plurality of solvents and solutes. The solute is a metal, polymer, other materials, or mixtures of materials. The solute may be a functional or ornamental material. Each ink droplet may be ejected onto a target area of a patterned substrate. After the droplets lands, the solvent evaporates and a thin film of the solute is formed. Controlling the final pattern of the solute film is essential to assuring the quality and repeatability of the printing process. In order to control the final pattern of the solute film, it is crucial to understand how the final pattern is formed. Understanding the influence of factors such as the evaporation rate, the initial droplet volume, the shape, the initial solute concentration and the contact line dynamics are crucial in controlling the final pattern. Numerical simulations of the printing process are useful tools for understanding the influence of these factors and for developing the control process for printing.
In the later stage of the ink drying process the aspect ratio of the droplet (the length of the droplet vs. the height of the droplet) increases and becomes quite large. Lubrication theory, which is good for describing the physics of thin films, may be applied to describe the evaporation physics and greatly reduce the complexity of the simulation at the later stage of the ink drying process. Lubrication theory is an approximation of the Navier-Stokes equation for thin films. The application of lubrication theory results in a fourth-order interface evolution equation. The fourth-order interface evolution equation describes the evolution of droplet surface considering the effects of evaporation rate, surface tension, and fluid viscosity. Prior art methods have solved these equations on a flat geometry and assumed that the droplet would take the form of a spherical cap. This assumption is invalid when the surface is not flat.
The present invention is a system and method for simulating the evaporation of a droplet on a non-flat surface using lubrication theory.